The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the digitization of NMR signals.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins after the excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G.sub.x G.sub.y and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The digitized, time domain, NMR signal corresponds to the spatial frequency representation of the object being imaged. This places some non-intuitive requirements on the sampling resolution of the analog-to-digital converter ("ADC"). If it is assumed that the object being imaged uniformly fills the field-of-view of the acquired image data set, the image signal to noise ("SNR"), for a 3D MR acquisition may be expressed as ##EQU1## where k is a system constant, N.sub.x, N.sub.y, & N.sub.z are the number of image pixels in the x, y and z direction respectively, v.sub.cc is the voxel volume, and r.sub.bw is the receiver bandwidth. The NMR signal's SNR, at the point where it has the maximum amplitude, is given by ##EQU2## Hence, the SNR of the image may be expressed as follows: ##EQU3##
A 16 bit ADC sampling the NMR signal has a resolution of .+-.32768 at the peak of the signal. However if one considers a 2D acquisition of a 256.times.256 sampling matrix (N.sub.x =256, N.sub.y =256, N.sub.z =1), then the maximum image SNR is just .+-.128. Typically, for 2D imaging, the image SNR is less than this, so presumably the limiting SNR factors lie elsewhere
Now consider a 3D acquisition. With a rapid imaging sequence it is possible to collect a full 3D volume, consisting of isotropic voxels in under 3 minutes. However, for a 256.times.256.times.256 sample acquisition, the maximum obtainable image SNR is limited by the 16 bit ADC to just .+-.8. To bring the 3D image SNR limit up to .+-.128 would require a 20 bit ADC which is very costly.